Born in Šempeter pri Gorici, he spent his childhood in Nova Gorica, Slovenia. Birsa's career began at the age of five, when he started playing for ND Bilje, the village club of Bilje near Nova Gorica. As he was a talented player, he was soon transferred first to Primorje, then to Gorica at the age of 17. By the second season he was already the second best striker and one of the best in the Slovenian first league, scoring 29 goals for his home team, an outstanding goalscoring record for a midfielder.
In 2006, he signed for French club Sochaux in Ligue de Football Professionnel, Ligue 1. He was declared the best Slovenian player of 2006–2008 by the leading Slovenian football website.
On 22 January 2009, AJ Auxerre signed him on a loan deal until June 2009 from Sochaux. He scored his first Auxerre goal against giants Lyon. On 29 May, it was announced that Auxerre had made the loan permanent. In the 2010–11 season, Birsa scored a 23-yard free kick and his first Champions league goal against Ajax in the group stage, Ajax eventually won 2–1.
On 2 February 2011, despite interest from big Premier league teams such as Liverpool and Fulham, Birsa signed a four-year contract with Serie A club Genoa. He made just nine appearances in his maiden season in Italy.
He joined Torino on the 31 August 2012 on loan. At Torino, Birsa played 17 games, scoring 2 goals but did not do enough to convince Torino to sign him on a permanent deal so he returned to Genoa at the end of the season.
Birsa made the switch to Milan on 31 August 2013, in what was a straight swap deal which saw Luca Antonini move in the opposite direction. He was handed the number 14 shirt at Milan. He scored his first goal for Milan on 28 September 2013 against Sampdoria to give the Rossoneri the win.
He signed for Chievo on 9 July 2014 on loan. On 2 July 2015, Chievo signed Birsa outright in a three-year contract.
He plays for the Slovenian national football team since 2006. He scored his first goal for the national team on 9 September 2009 in a World Cup qualifying match against Poland, which Slovenia won 3–0. At the 2010 World Cup finals, Birsa struck a long-range curling shot in Slovenia's second match against the United States. Slovenia drew that match 2–2.As of 18 May 2016
Scores and results list Slovenia's goal tally first.
Birsa was born in Šempeter pri Gorici, present day Slovenia. He is a childhood friend of three professional footballers, Etien Velikonja, Tim Matavž and Goran Cvijanović, who also lived in the same town. In 2012, he married his long-time girlfriend Mateja, the couple has a son named Nolan.Slovenian PrvaLiga: 2004–05, 2005–06
Coupe de France: 2006–07